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Mathematics 15 Online
OpenStudy (angelax0):

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OpenStudy (angelax0):

OpenStudy (angelax0):

@jhonyy9

jhonyy9 (jhonyy9):

you need substituting the x+2 in place of x inside this function

OpenStudy (angelax0):

so 6(x+2)^2 - 7(x+2) ?

OpenStudy (angelax0):

6x^2+4 -7x+14 ?

jhonyy9 (jhonyy9):

no first (x+2)^2 = ?

jhonyy9 (jhonyy9):

do you know formula of (a+b)^2 = ?

OpenStudy (angelax0):

no i dont

jhonyy9 (jhonyy9):

(a+b)^2 = (a+b)(a+b) = ?

OpenStudy (angelax0):

a^2+b^2 ?

jhonyy9 (jhonyy9):

no no

jhonyy9 (jhonyy9):

(a+b)(a+b) = a*a +a*b + b*a + b*b = ?

OpenStudy (angelax0):

a^2 + ab + ba + b^2 ?

jhonyy9 (jhonyy9):

ab = ba yes ?

OpenStudy (angelax0):

yes

jhonyy9 (jhonyy9):

so than these two terms what will result ?

OpenStudy (angelax0):

a^2 and b^2 ?

jhonyy9 (jhonyy9):

no than you see that there are a^2 +ab +ba +b^2 and you know that ab=ba

jhonyy9 (jhonyy9):

will result a^2 +ab +ab +b^2 = ?

OpenStudy (angelax0):

im not sure

OpenStudy (angelax0):

2a and 2b?

jhonyy9 (jhonyy9):

there are two of ab how you can write this ? dont separate the a from b bc. there is a multiply b

OpenStudy (angelax0):

2(ab)

jhonyy9 (jhonyy9):

yes sure 2ab without parentheses

jhonyy9 (jhonyy9):

so you know now that (a+b)^2 = a^2 +2ab +b^2

OpenStudy (angelax0):

yes

jhonyy9 (jhonyy9):

use this formula in this case of your exercise

OpenStudy (angelax0):

6(x+2)^2 = 6^2+2x+2+2^2 ?

jhonyy9 (jhonyy9):

without this 6 firstly (x+2)^2 = ?

OpenStudy (angelax0):

x^2 + 2x+2 + 2^2

jhonyy9 (jhonyy9):

the midle term not is right there is (a+b)^2 = a^2 +2ab +b^2 so (x+2)^2 = ?

jhonyy9 (jhonyy9):

a=x and b=2

OpenStudy (angelax0):

x^2 + 2^2

jhonyy9 (jhonyy9):

no you forgot the 2ab

OpenStudy (angelax0):

2x+2

OpenStudy (angelax0):

x+2^2

jhonyy9 (jhonyy9):

2 time a time b

OpenStudy (angelax0):

2(x2)

jhonyy9 (jhonyy9):

2*x*2 but you know that 2*x*2 = 2*2*x = ?

OpenStudy (angelax0):

yes

jhonyy9 (jhonyy9):

so equal ?

OpenStudy (angelax0):

4x

jhonyy9 (jhonyy9):

and now how will be (x+2)^2 = ?

OpenStudy (angelax0):

x*2*2

OpenStudy (angelax0):

x^2 + x*2*2 + 2^2

jhonyy9 (jhonyy9):

but the midle term you wrote it above that is equal 4x

OpenStudy (angelax0):

so would it be x^2 + 4x + 2^2

jhonyy9 (jhonyy9):

and 2^2 = ?

OpenStudy (angelax0):

4

jhonyy9 (jhonyy9):

so than how will be there 6(x+2)^2 = ?

OpenStudy (angelax0):

6(x^2+4x+4)

jhonyy9 (jhonyy9):

perfect - very nice - but now you need distribute the parentheses

OpenStudy (angelax0):

so 36x^2+24x+24 ?

jhonyy9 (jhonyy9):

why 36 ? you need multiply just the 6 by x^2

OpenStudy (angelax0):

6x^2

jhonyy9 (jhonyy9):

yes and there is again 7x where you need substituting again too the (x+2) in place of x so what will result ?

OpenStudy (angelax0):

7x+14?

jhonyy9 (jhonyy9):

yes and now please wrote completly the denominator what you ve got

jhonyy9 (jhonyy9):

please write - sorry

OpenStudy (angelax0):

6x^2 + 24x + 24 - 7x + 14

jhonyy9 (jhonyy9):

why plus 14 when you multiply the -7 by 2 = ?

OpenStudy (angelax0):

-14

jhonyy9 (jhonyy9):

yes please correct it

OpenStudy (angelax0):

6x^2 + 24x + 24 - 7x - 14

jhonyy9 (jhonyy9):

and now assume the same terms

OpenStudy (angelax0):

6x^2 + 17x + 10

jhonyy9 (jhonyy9):

yes so this will be the denominator of this resulted fraction and now how will be completly f(x+2) = ?

OpenStudy (angelax0):

im not sure

jhonyy9 (jhonyy9):

courage please i m here to help you

OpenStudy (angelax0):

9 / 6x^2 + 17x + 10 ???

jhonyy9 (jhonyy9):

ok but how you write it more understandably 9 f(x+2) = --------------- ?

OpenStudy (angelax0):

9 / 10 ?

jhonyy9 (jhonyy9):

why just 10 ?

jhonyy9 (jhonyy9):

i ve said you that this quadratic equation will be the denominator of this fraction

OpenStudy (angelax0):

i dont know

jhonyy9 (jhonyy9):

9 / 6x^2 + 17x + 10 so this mean 9/(6x^2 + 17x + 10 ) please believe me

jhonyy9 (jhonyy9):

9 f(x+2) = ------------------ ( 6x^2 + 17x + 10 ) ok. this is the right answer sure

OpenStudy (angelax0):

so do i need the parenthesis around it?

jhonyy9 (jhonyy9):

not are necessarly

OpenStudy (angelax0):

thank you

jhonyy9 (jhonyy9):

np wa my pleasure hope you understand it - yes ?

OpenStudy (angelax0):

yes

jhonyy9 (jhonyy9):

ok good luck bye bye

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